Wagner logged birdies on three of his first five holes to seize the lead and stayed atop the pack most of the day, ending at 14-under 196. The former Virginia Tech star will be seeking his fourth PGA Tour title in Sunday's final round.
His stiffest challenge will likely come from Jimmy Walker, who also notched a 64 to finish the third round two strokes back at minus-12.
Jonas Blixt ended the day with sole possession of third at 10-under with a round of 3-under 67. Matt Jones moved up 13 spots for a fourth-place tie one shot farther back with a 4-under 66.
Jordan Spieth (67) and Steven Bowditch (69) also earned a share of fourth at minus-9.
Overnight leader Matt Every, meanwhile, stumbled to a 4-over 74, dropping 26 spots on the leaderboard to nine shots off the pace.